USC Predict COVID Project: Predictive Epidemic Model for COVID-19 in Los Angeles County
Abigail Horn, PhD1, Lai Jiang, MS, Wendy Cozen, MD, David Conti, PhD
4/24/2020
Updated with data available as of April 25, 2020
Summary
Aims
The USC Predict COVID project is using an epidemic model to estimate the impact of COVID-19 in Los Angeles County
We are addressing the key questions of:
- When will the peak of the epidemic occur and how will it impact health care capacity?
- What happens to the dynamics of the epidemic when social distancing ends?
- How will the epidemic affect different at-risk groups?
Why our model is unique
- Our epidemic compartmental model uses stochastic differential equations and approximate Bayes calculation techniques for parameter estimation.
- Importantly, the model presents the uncertainty in all estimations and predictions.
- We incorporate prior information for parameter specification.
- We incorporate risk factors (e.g. advanced age, existing health conditions) into the analysis.
- We can modify parameters at different time points, enabling the specification of interventions, e.g. social distancing scenarios
Predictions and Estimation
(1) Critical healthcare variables predicted by the model are the counts of the numbers of individuals over time, including the peak occurrence, for the following:
- The total number of infected cases including both the number detected and observed with testing and the undetected/untested cases
- The total number of individuals hospitalized (including those in the ICU)
- The number of patients in the ICU
- The number of patients on ventilators
- The number of deaths
(2) We estimate a number of key epidemic parameters, including:
- \(R0\), the reproductive number or average number of new infections generated by an infected person in a completely susceptible population
- \(r\), the proportion of illnesses that are detected and reported out of all illnesses
- \(Frac_{R0}\), the reduction in the initial R0 due to social distancing
- \(\alpha\), the probability of hospitalization given illness, i.e. \(Pr(Hospital | Illness)\)
- \(\kappa\), the probability of ICU care necessary given hospitalization, i.e. \(Pr(ICU | Hospital)\)
- \(p_v\), the probability of ventilation given ICU care, i.e. \(Pr(Ventilation | ICU)\)
- \(\delta\), the probability of death given ICU care, i.e. \(Pr(Death | ICU)\)
Projections
Current Projections: Summary of Key Model Estimated Variables
| Median | Upper 50 CI | Lower 50 CI | |
|---|---|---|---|
| Peak Hospitalizations | 6,086.00 | 9,727.00 | 2,558.00 |
| Deaths by August 1, 2020 | 21,562.50 | 31,506.25 | 12,798.75 |
| Detected Illnesses by August 1,2020 | 622,988.00 | 900,654.75 | 362,311.00 |
| Total Illnesses by August 1, 2020 | 5,428,588.50 | 6,715,058.50 | 3,217,905.50 |
| Proportion of Cases Detected (%) | 13.22 | 16.04 | 10.45 |
| CFR Based on Observed Illnesses (%) | 3.87 | 4.74 | 2.78 |
| CFR Based on Total Illnesses (%) | 0.48 | 0.62 | 0.35 |
| R0 - before social distancing | 3.38 | 3.79 | 2.96 |
| % Reduction in Social Contacts (March 15 - ) | 59.82 | 54.26 | 63.59 |
Current Projections: Illnesses, Hospitalizations, ICU Admittances, Ventilation Requirements, Deaths
Dashed line = Maximum possible capacity (i.e., total licensed hospital beds, ICU beds, ventilators) in L.A. County
Model Fits Against Data
Demonstrating model fit against COVID-19 data for Los Angeles, for the following variables:
- Observed illnesses, cumulative
- Hospitalizations, cumulative
- Hospitalization, daily new incidence
- Ventilation, cumulative
- Deaths, cumulative
- Deaths, daily new incidence
COVID-19 data is shown as black dots in the figures below.
Comparing Social Distancing Mitigation Strategies
- Model projections forecast that, if everything continutes as is, LA is not going to see a sharp peak in illnesses in the near future, and rather will see a long, shallow, manageable epidemic curve over the next number of months.
- What can we do to maintain this manageable epidemic curve while sustaining a functioning society?
- Here we evaluate the effect of scenarios relating to social distancing on the ultimate epidemic trajectory
Scenario Comparison
Comparison between current level of social distancing of ~50% beginning March 15, 2020 and counterfactual: if social distancing had never been implemented 
Comparison between current level of social distancing of ~50% beginning March 15, 2020 and easing of social distancing from 50% to 25% on May 1, 2020 
Comparison between current level of social distancing of ~50% beginning March 15, 2020 and easing of social distancing from 50% to 25% on June 1, 2020 
Comparison between current level of social distancing of ~50% beginning March 15, 2020 and easing of social distancing from 50% to 25% on July 1, 2020 
Comparison between current level of social distancing of ~50% beginning March 15, 2020 and removal of social distancing on June 1, 2020 
Comparison between policy of easing of social distancing from 50% to 25% on June 1, 2020 and gradual easing beginning June 1, 2020 of social distancing from 50% to no social distancing 
Projections by Key Risk Groups and Risk Factors
We analyze how population prevalence of known COVID-19 risk factors: advanced age, existence of other health conditions or comorbidities, smoking status, and obesity status, affect COVID-19 illness trajectories in L.A. County and spatial subdivisions.
First, we estimate the conditional probability of COVID illness severity given combinations of risk factors. We categorize the population into a number of risk profiles, representing different combinations of known COVID-19 risk factors: advanced age, existence of other health conditions or comorbidities, smoking status, and obesity status. Using previous COVID-19 studies reporting the marginal risk of severe COVID-19 outcomes given individual risk factors, we develop a statistical model to estimate the probability of COVID illness trajectories for individuals having or not having combinations of risk factors represented by these risk profiles. Specifically, we estimate the probability that individuals within a specific risk group are admitted to hospital given having acquired illness \(Pr(Hospital | Illness, Profile_i)\), are admitted to the ICU given admittance to hospitalized \(Pr(ICU | Hospital, Profile_i)\), and that die given being admitted to the ICU \(Pr(Death | ICU, Profile_i)\). More information is provided below under Methods and Data.
For the analysis below, we have grouped the multiple risk profiles into 5 key risk groups according to similar within-group levels of the probabilities \(Pr(Hospital | Illness, Profile_i)\), \(Pr(ICU | Hospital, Profile_i)\), and \(Pr(Death | ICU, Profile_i)\).
Second, we use these probabilities to estimate the proportion of each risk group that will make up the resulting cohorts of COVID patients admitted to hospital, admitted to ICU, or that die within the L.A. County population, based on the prevalence of each risk group in the population.
Results are also presented for each Service Planning Area (SPA) population within L.A. County. A SPA is a specific geographical region within Los Angeles County used by the Department of Public Health to plan and provide health services. There are 8 SPAs in Los Angeles County.
Risk Profiles, Risk Factors, and Risk Groups
- The following table presents the model-estimated probabilities \(Pr(Hospital | Illness,Profile_i)\), \(Pr(ICU | Hospital,Profile_i)\), and \(Pr(Death | ICU,Profile_i)\) for each risk group (or combination of risk factors), as well as the prevalence of these risk groups/factors in the general L.A. County Population \(Pr(Profile_i)\).
5 Risk Groups by Stage of Disease and SPA
- These figures show the estimated proportion of each risk group that will make up the resulting cohorts of COVID patients admitted to hospital, admitted to ICU, or that die within the L.A. County/SPA population, based on the population prevalence of the risk group in L.A. County/SPAs.
- The analyses are presented for each risk group, as well as stratified to the individual risk factors (age, comorbidities, obesity status, smoking status).
Key Risk Factors by Stage of Disease
Trajectories: Hospitalizations, ICU, Deaths by Key Risk Factors LA County
Trajectories: Broken down by key risk factors for LA County
Parameter estimates
Model estimated parameters and prior information
Here we summarize our estimated parameter values for key epidemic and model quantities:
- \(R0\), the reproductive number or average number of new infections generated by an infected person in a completely susceptible population
- \(r\), the proportion of illnesses that are observed
- \(Frac_{R0}\), the reduction in the initial R0 due to social distancing
- \(\alpha\), the probability of hospitalization given illness, i.e. \(Pr(Hospital | Illness)\)
- \(\kappa\), the probability of ICU care necessary given hospitalization, i.e. \(Pr(ICU | Hospital)\)
- \(p_v\), the probability of ventilation given ICU care, i.e. \(Pr(Ventilation | ICU)\)
- \(\delta\), the probability of death given ICU care, i.e. \(Pr(Death | ICU)\)
Because our model is stochastic and we are using Bayesian techniques for parameter estimation, each posterior parameter estimate is represented by a distribution of likely values.
This table summarizes key statistics of each estimated parameter: the mean and the standard deviation (sd).
| R0 | Prop. cases detected (r) | Frac R0 Mar11 | Pr(Death|ICU) | Pr(Hospital|Illness) | Pr(ICU|Hospital) | Pr(Ventilation|ICU) | Frac R0 Apr23 | |
|---|---|---|---|---|---|---|---|---|
| mean | 3.36 | 0.14 | 0.42 | 0.54 | 0.21 | 0.36 | 0.74 | 0.40 |
| sd | 0.61 | 0.05 | 0.06 | 0.16 | 0.03 | 0.04 | 0.08 | 0.06 |
- Mean = 3.36
- Standard deviation = 0.61
Information informing prior distribution - \(R0\) prior estimate is based on values for \(R0\) estimated from other published studies on COVID-19.
- Mean = 0.14
- Standard deviation = 0.05
- Mean = 0.42
- Standard deviation = 0.06
Information informing this parameter’s prior distribution:
We use mobility data to narrow the specification of the reduction in the average number of new infections due to an infected person (R0) in a completely susceptible population under recent social distancing restrictions.
Effectively, reductions in mobility correspond to a proportional reduction in R0
Reduction in mobility observed in LA County:
Source: Assessing changes in commuting and individual mobility in major metropolitan areas in the United States during the COVID-19 outbreakOur modeled reduction in R0 timeline:
We use previous studies to narrow the specification of the probability of hospitalization given illness, admittance to the intensive care unit (ICU) given being in hospital, ventilation given being in ICU, and death given being in ICU by incorporating risk factors, including age, sex, smoking and other comorbidities. The prevalence of these risk factors in Los Angeles County is also included.
Studies on COVID-19 clinical presentation and trajectories to inform the probability of hospitalization, ICU, and ventilation based on single risk factors: - Guan, Wei-jie, et al. “Clinical characteristics of coronavirus disease 2019 in China.” New England Journal of Medicine (2020). - Petrilli, Christopher M., et al. “Factors associated with hospitalization and critical illness among 4,103 patients with COVID-19 disease in New York City.” medRxiv (2020).
Prevalence data sources: - Los Angeles County Health Survey - UCLA California Health Information Survey
- Mean = 0.21
- Standard deviation = 0.03
- Mean = 0.36
- Standard deviation = 0.04
- Mean = 0.54
- Standard deviation = 0.16
- Mean = 0.74
- Standard deviation = 0.08
